These are actually leaffooted bugs. They target pomegranates amongst other things. I think the neem oil that Chris suggested might work, but unlike squash bugs, these guys will often fly away right as you're getting to them.
Rachel is correct, they are, indeed, leaf-footed bugs. When you posted the pic, I googled them, because they are somewhat similar to assassin bugs. Last year, my pomegranates were inundated with leaf footed bugs. We experienced a lot of fruit drop, and the chickens feasted heartily. This year, I have noticed very few of them, and the fruit drop has lessened significantly. I do believe the chickens are eating the nymphs. I doubt they'd eat the adults, as they are also called stink bugs.
Leaf-footed bugs have long sucking mouthparts that they use to suck the juice from seeds that don't have a hard coat which is why they really love pomengranates. They overwinter as adults in weeds or debris piles so clean up the area around your pomengranates. I staple paperbags over my immature pomengranates to keep the bugs off - but like Anita, I have had far fewer leaf-fotted bugs this year since I got chickens so I too am assuming that many of the nymphs became chicken treats. The nymphs are bright red and black and have a much smaller 'foot'. I handpick any adults I see and drop them in soapy water - just like squash bugs.
Interesting how what works for some doesn't work for others. I would go for the paper bags, what can it hurt? Our pomegranate tree is really old, so we have an over-abundance of fruit, and I don't mind sharing with the wildlife. I also have been picking the fruit that is damaged and feeding it to the chickens. Perhaps that's how all of the nymphs are being eaten.
On the other hand, I have lots of leaf-footed bugs in my front yard; they seem to be partial to the sunflower out there. But now I'm starting to notice them spreading to my pepper plants. I think I'll do the soapy water shake method, now that I've got positive identification as a pest. There is an abundance of black beetles on the plants out there as well, I'm having problems getting a clear enough picture for positive identification ...
My pomegranate is just a few years old - I didn't have adult leaf-footed bugs until last fall (when I actually had more than a handful of fruit growing) and then the nymphs appeared this spring so maybe your chickens will get some nymph treats next year... I would try paper bags on poms that haven't been punctured yet by the bugs - you might be able to save some for yourself. Hand picking of the adults seems to work best for me at dawn or dusk - they don't seem to fly away as fast as they do during the daytime.